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CFD
Particuology 10 (2012) 229–235
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Particuology journal homepage: www.elsevier.com/locate/partic
Modelling die filling with charged particles using DEM/CFD Emmanuel Nkem Nwose, Chunlei Pei, Chuan-Yu Wu ∗ School of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK
a r t i c l e
i n f o
Article history: Received 4 October 2011 Received in revised form 22 November 2011 Accepted 26 November 2011 Keywords: DEM CFD Electrostatics Die filling Powder flow Cohesion Charged particles
a b s t r a c t The effects of electrostatic charge on powder flow behaviour during die filling in a vacuum and in air were analysed using a coupled discrete element method and computational fluid dynamics (DEM/CFD) code, in which long range electrostatic interactions were implemented. The present 2D simulations revealed that both electrostatic charge and the presence of air can affect the powder flow behaviour during die filling. It was found that the electrostatic charge inhibited the flow of powders into the die and induced a loose packing structure. At the same filling speed, increasing the electrostatic charge led to a decrease in the fill ratio which quantifies the volumetric occupancy of powder in the die. In addition, increasing the shoe speed caused a further decrease in the fill ratio, which was characterised using the concept of critical filling speed. When the electrostatic charge was low, the air/particle interaction was strong so that a lower critical filling speed was obtained for die filling in air than in a vacuum. With high electrostatic charge, the electrostatic interactions became dominant. Consequently, similar fill ratio and critical filling speed were obtained for die filling in air and in a vacuum. © 2012 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1. Introduction Powders are common materials handled in various industries, such as food, chemical, metallurgical, pharmaceutical, agricultural and ceramic industries (Wu, 2008). It is well recognised that a number of factors, such as powder properties, processing conditions and the equipment design, affect powder flow behaviour (Schneider, Sinka, & Cocks, 2007). For instance, mixing powders in a humid environment will potentially cause stickiness and could lead to agglomeration and consequently degradation of products. In addition, during powder handling and processing, the use of multiple blends of crystalline powders and the inclusion of additives make powder blends prone to be electrostatically charged through contact electrification and polarisation (Bailey, 1984, 1993; Elsdon & Mitchell, 1976; Engers, Fricke, Newman, & Morris, 2007; Pingali, Shinbrot, Hammond, & Muzzio, 2009). In a number of powder handling processes, such as hopper discharge, grinding, sieving, mixing, fluidisation and conveying, the electrostatic charge can be transferred from a particle to its neighbouring particles or walls through the exchange of electrons, ions or materials (Matsusaka, Maruyama, Matsuyama, & Ghadiri, 2010). Once the particles in a powder get charged, attraction or repulsion can occur due to electrostatic interactions. The electrostatic
∗ Corresponding author. Tel.: +44 121 4145365; fax: +44 121 4145324. E-mail address: [email protected] (C.-Y. Wu).
interaction, on one hand, can be utilised to facilitate processing of powders, for example, in gas cleaning using electrostatic precipitators (Jaworek, Krupa, & Czech, 2007) and electrostatic coating (Takeuchi, 2008). On the other hand, it can lead to detrimental consequences, such as increasing the flow instability of powders as frequently observed in practice (Bailey, 1984; Engers et al., 2007; Glor, 1985; Pingali et al., 2009), and dust explosion due to the accumulation of excessive electrostatic charges (Bailey, 1993; Glor, 1985). It is hence necessary to consider the effect of electrostatics in powder handling and processing practice, as demonstrated by Matsusaka and Masuda (2006), who showed that the inclusion of electrostatic charges gave a better approximation of the apropos powder flow rate through a pipe. It is well recognized that the powder flow behaviour during die filling controls the quality of products manufactured through powder compaction (Bocchini, 1987; Hjortsberg & Bergquist, 2002; Rice & Tengzelius, 1986; Schneider et al., 2007; Wu, 2008; Wu, Dihoru, & Cocks, 2003), which is a typical manufacture process in pharmaceutical, ceramic and powder metallurgy industries, and typically involves three distinctive stages: die filling, compaction and ejection (Wu, 2008). Although die filling has been intensively investigated experimentally and numerically (Bierwisch, Kraft, Riedel, & Moseler, 2009; Guo, Kafui, Wu, Thornton, & Seville, 2009; Guo, Wu, Kafui, & Thornton, 2010; Guo, Wu, Kafui, & Thornton, 2011; Guo, Wu, & Thornton, 2011; Schneider et al., 2007; Wu, 2008; Wu et al., 2003; Wu & Guo, 2010), little attention has been paid to how electrostatics affects the powder flow behaviour during die
1674-2001/$ – see front matter © 2012 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.partic.2011.11.010
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filling. Therefore, in this study, the flow of charged powders during die filling was explored using a modified DEM/CFD, in which long range electrostatic interactions were considered. How the electrostatic charge affects the powder behaviour during die filling was examined in detail.
2. DEM/CFD DEM/CFD is a coupled numerical method that adapts an Eulerian–Lagrangian approach in modelling solid/gas and solid/fluid two phase particulate flows (Kafui, Thornton, & Adams, 2002; Tsuji, Kawaguchi, & Tanaka, 1993; Yu & Xu, 2003). In DEM/CFD, the motion of particles is modelled using DEM while the flow of gases or fluids is solved using CFD. The interactions between particles and gases/fluids are considered and two-way coupling is implemented so that how the motion of particles affects the gas or fluid flow is considered, so is the effect of fluid flow on the motion of particles. The DEM/CFD has been approved as a robust method for modelling two phase flows involving particles (Guo et al., 2009, 2010; Guo, Wu, Kafui, et al., 2011; Guo, Wu, et al., 2011; Kafui et al., 2002; Tsuji et al., 1993; Wu & Guo, 2010; Yu, Guo, & Wu, 2009; Yu & Xu, 2003). It has also been successfully used to model die filling in the presence of air (Guo et al., 2009, 2010; Guo, Wu, Kafui, et al., 2011; Guo, Wu, et al., 2011; Wu & Guo, 2010). In addition, DEM was also modified to model flow of charged particles (Hogue, Calle, Weitzman, & Curry, 2008; Pei, Wu, Byard, & England, 2010; Watano, 2006). Watano (2006) developed a DEM with a simplified electrification model that assumes the charge of a particle to be proportional to the normal contact velocity and the number of collisions, and explored the flow of electrostatically charged powder in a pneumatic conveyor system. Hogue et al. (2008) analysed the flow of particles rolling down an inclined plane using a DEM with a time-dependent electrification model. Pei et al. (2010) incorporated electrostatic interactions into the DEM/CFD developed by Kafui et al. (2002) and modelled the deposition of charged particles in a tube in the presence of air.
2.1. DEM/CFD with electrostatics In this study, the model developed by Pei et al. (2010) was employed to model the die filling with charged particles. The interactions between elastic particles are modelled using Hertz theory in the normal direction and the theory of Mindlin and Deresiewicz in the tangential direction (Kafui et al., 2002). In this modified DEM/CFD model, a truncation method with a pre-defined cut-off distance is implemented for detecting the long-range electrostatic interactions between objects. When the distance between two objects is larger than the cut-off distance, the electrostatic interaction is ignored, which is similar to those employed by others (Hogue et al., 2008; Watano, 2006). Within the cut-off distance, the electrostatic force between particles is modelled using the Coulomb’s law (Seville, Tuzun, & Clift, 1997) as follow: F21 =
1 q1 q2 rˆ 21 , 4ε0 εr r 2 21
(1)
where F21 is the electrostatic force from particle 2 to particle 1, ε0 is the permittivity of free space, εr is the relative permittivity of the medium in the vicinity of the particles, q1 and q2 are the values of charges on the two particles, r21 is the distance between the r21 is the unit vector from particle centres of the two particles and ˆ 2 to particle 1.
Fig. 1. Model set up for die filling.
The interaction between a charged particle and a surface within the cut-off distance is modelled using an imaging force (Seville et al., 1997): Fimg =
1 Q2 aˆ , 4ε0 εr (2a)2
(2)
where Fimg is the image force of the particle towards the neutral inductive surface, Q is the value of the charges on the particle, a is the distance between the centre of the particle and the neutral ˆ is the unit vector from the particle to the inductive surface and a neutral inductive surface. Using the truncation method, it is critical to set an appropriate cut-off distance as the longer the cut-off distance, the more accurate the electrostatic interaction is modelled, but the more expensive the computation is. Although a short cut-off distance leads to faster computing, it may induce significant numerical errors as a large amount of electrostatic interactions is ignored. In this study, the cut off distance is set to 10 times the particle radius, which is sufficiently large for the cases considered. The Newton’s equation of motion was used to calculate the velocity, position and acceleration of the particles once all interaction forces, including the long-range electrostatic forces, mechanical contact forces, air-drag forces and so on, are determined. 2.2. DEM/CFD model for die filling The modified DEM/CFD model with electrostatic interaction was used to simulate die filling in air and in a vacuum in 2D, which is less computation intensive and easier for data visualising and process understanding, compared to 3D simulations. The DEM/CFD model for die filling is shown in Fig. 1. The model consisted of a shoe (9.0 mm wide and 14.0 mm high), and a die (2.0 mm wide and 3.0 mm high). In this study, only passive die filling (i.e. a moving shoe was utilised while the die remained stationary) was analysed. The shoe sat above a platform and moved from right to left at a specified filling speed ranging from 0.08 to 0.40 m/s in this study, which was similar to the typical die filling speed used in practice (Wu, 2008). The powder was modelled as an assembly of mono-sized particles of 100 m in diameter. Die filling simulations with 1000 mono-sized particles were reported here. Preliminary studies with 5000 particles for some typical cases were also performed and similar results were obtained. It was believed that 1000 particles were sufficient for the cases considered here. For die filling
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Table 1 Simulation parameters. Parameter Particle properties Particle diameter (m) Particle density (kg/m3 ) Young’s modulus (Pa) Poisson’s ratio Vessel properties Density (kg/m3 ) Young’s modulus (Pa) Poisson’s ratio Interaction properties Inter-particle friction coefficient Particle/wall friction coefficient Gas properties Shear viscosity (Pa s) Temperature (K) Average molar mass (kg/mol) Pressure (Pa)
Value 100 1500 8.70 × 109 0.30 7900 210 × 109 0.30 0.30 0.30 1.8 × 10−5 293 2.88 × 10−2 1.01325 × 105
with charged particles, 500 particles were assumed to be charged positively, while the other 500 were negatively charged. In each simulation, all particles had the same magnitude of charge. In order to explore the influence of electrostatic charge on die filling behaviour, the particle charge was systematically varied between 0.0 and 1.0 × 10−12 C, which are the typical values of charges that pharmaceutical powders acquire during the handling processes (Rowley, 2001; Watanabe et al., 2007). For the particles, material properties of microcrystalline cellulose (MCC) were used, while the shoe, the die and the platform were assumed to be stainless steel. The simulation parameters are listed in Table 1. The explicit time step is 0.227 × 10−7 s. For the highest electrostatic charge (10 × 10−13 C) used in this study, the electrostatic force at its cutoff distance is more than 20 times smaller than the gravity of the particle. The particles were initially generated randomly inside the shoe and then settled onto the bottom of the shoe under gravity and electrostatic forces (for charged particles only). Once the particles settled in the shoe with a negligible kinetic energy, the shoe started to move at the specified filling speed. When it traversed over the die, some particles were deposited into the die. The simulation was terminated once the shoe passed the die and the deposited particles settled. 3. Results and discussion From DEM/CFD simulations, the positions and kinematics of individual particles were determined at different time instants, from which the overall flow patterns were obtained. The typical powder flow patterns are presented in Figs. 2–5. In addition, the average mass flow rate was determined by tracking the particles deposited into the die. Knowing the positions and the total number of deposited particles enabled the fill ratio, a parameter that was introduced to characterise the die filling behaviour (Sinka, Schneider, & Cocks, 2004; Wu, 2008; Wu & Cocks, 2006; Wu et al., 2003), to be determined. In this section, the effect of electrostatic charge on powder flow patterns during die filling was discussed, followed by an examination of the effect on the fill ratio. 3.1. Powder flow patterns The powder flow pattern during die filling with uncharged particles (q = 0 C) in air at a filling speed of 0.1 m/s is shown in Fig. 2. It is evident that at this particular speed a ‘nose’ shaped profile was formed when the powder in the shoe is delivered just over the die opening (Fig. 2(a)). This was defined as the nose flow by Wu et al. (2003), with which particles located at both the top free
Fig. 2. Powder flow patterns during die filling with un-charged particles (q = 0 C) in air at a filling speed of 0.1 m/s.
surface and the bottom of the powder bed were deposited into the die. As the shoe moved further, the flowing powder stream hit the far side of the die (the left wall) and flowed backwards (Fig. 2(b) and (c)). After the shoe passed the die opening, the die was almost completely filled (Fig. 2(d)). Although a similar powder flow pattern was observed for the die filling in a vacuum with the same powder at the same filling speed (Fig. 3), comparing Fig. 3 with Fig. 2 does reveal that the powder flow in a vacuum was faster than in air and more particles are deposited into the die in a vacuum (see Figs. 2(d) and 3(d)), indicating that the presence of air inhibits the powder flow during die filling. All these observations are in broad agreement with the experimental observations reported in the literature (Schneider et al., 2007; Wu & Cocks, 2006; Wu et al., 2003). As the filling speed was increased from 0.1 m/s (Fig. 2) to 0.2 m/s (Fig. 4), the powder bed in the shoe strode over the die opening quickly and covered the die (Fig. 4(a)). Consequently, only particles located at the bottom of the powder bed were deposited along the far side (i.e. the left wall) into the die (Fig. 4(b) and (c)). This is the so-called “bulk flow” (Wu et al., 2003), with which the flow is slow and the die filling processes dominated with bulk flow generally led to a partially die fill (i.e. the die was not completely filled with particles). This is further demonstrated from the present DEM/CFD simulations, as it was clear that the die was only partially filled (Fig. 4(d)) when the filling speed was increased to 0.2 m/s. Once the particles were charged oppositely, the electrostatic interaction promoted the formation of clusters of particles carrying
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Fig. 3. Powder flow patterns during die filling with un-charged particles (q = 0 C) in a vacuum at a filling speed of 0.1 m/s.
Fig. 4. Powder flow patterns during die filling with un-charged particles (q = 0 C) in air at a filling speed of 0.2 m/s.
opposite charges, as shown numerically (Pei et al., 2010) and experimentally (Grzybowski, Winkleman, Wiles, Brumer, & Whitesides, 2003). This is also observed in the present die filling simulations with oppositely charged particles as illustrated in Fig. 5. It can be seen that localised particle clusters were formed in the powder bed. In addition, the strong image forces between charged particles and the surfaces of the shoe and the die caused some particle sticking on the surfaces, as commonly observed in the powder handling practice. In addition, the strong electrostatic forces significantly prevented the particles from flowing into the die, as the particles were only scraped and squeezed along the far side into the die (Fig. 5(b) and (c)). Furthermore, the deposited particles stuck on the die wall and formed very loose packing structure as shown in Fig. 5(d).
bed in the die is constant, i.e. independent of the filling speed and die fill level, Eq. (3) can be rewritten as
3.2. The effect of electrostatic charge on the fill ratio Wu et al. (2003) introduced the fill ratio to characterise the packing behaviour of powders during die filling. The fill ratio was defined as the ratio of the volume of the powder bed to the die volume (Schneider et al., 2007; Sinka et al., 2004; Wu, 2008; Wu et al., 2003), i.e. ı=
˚p , ˚d
(3)
where ˚p and ˚d are respectively the volume of the powder bed and of the die. A fill ratio of a value of unity indicates that the die is completely filled. Assuming that the bulk density b of the powder
ı=
Mp , Md
(4)
where Mp and Md are the total powder mass deposited in the die at a specified filling speed and the powder mass of fully filled die, respectively. Eq. (4) provides a simple approach to determine the fill ratio, which has been used to analyse both experimental and numerical data (Schneider et al., 2007; Sinka et al., 2004; Wu, 2008; Wu et al., 2003). The fill ratios for die filling with powders of different electrostatic charges at various filling speeds in a vacuum and in air are presented in Fig. 6. It can be seen that the fill ratio generally decreases as the filling speed (i.e. the shoe speed) increases. At the same filling speed, it is also observed that the fill ratio decreases as the electrostatic charge increases, indicating that a poorer flow performance and a more cohesive system were induced once the powder acquires more electrostatic charges. Comparing the data shown in Fig. 6(a) (in a vacuum) and (b) (in air) reveals that a lower fill ratio is generally obtained for die filling in air than in a vacuum. However, the difference between the fill ratios in a vacuum and in air decreases as the electrostatic charge is increased. This is due to the fact that the presence of air generally inhibits the flow of powder into the die so that a low fill ratio is obtained compared to the filling in a vacuum (Wu & Cocks, 2006; Wu et al., 2003). However, once the particles are charged oppositely, they form large clusters/agglomerates due to the attractive electrostatic force,
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Fig. 5. Powder flow patterns during die filling with oppositely charged particles (q = 1.0 × 10−12 C) in air at a filling speed of 0.1 m/s.
especially with high electrostatic charges. Consequently, the effect of air becomes insignificant as a result of the increased agglomerate sizes when the charge is sufficiently high. The variation of fill ratio with filling speed can be further characterised using the concept of critical filling speed, which was defined as the highest filling speed at which the die can be completely filled (Wu, 2008; Wu et al., 2003). In other words, the die cannot be completely filled (i.e. ı < 1) if the filling speed is higher than the critical filling speed, while it can be completely filled (i.e. ı = 1) if the speed is lower than the critical filling speed. We hence have ı = 1 for vs ≤ vc for vs > vc
ı < 1,
(5a) (5b)
where vs and vc are the filling (shoe) speed and critical filling speed, respectively. The critical filling speed is proved to be a useful parameter for characterising the flowability of powders during die filling (Schneider et al., 2007; Sinka et al., 2004; Wu et al., 2003). A higher critical filling speed indicates better flowability so that faster filling can be accomplished, while a lower critical filling speed implies poorer powder flowability and slower filling has to be employed to ensure complete fill of the die. For die filling at high speeds (vs ≥ vc ), Wu et al. (2003) developed a model assuming that powder flow into a die was a steady flow and proposed that the fill ratio can be related to the filling speed and the critical filling speed by ı=
v n c
vs
,
for vs = vc
(6)
Fig. 6. Variation of filling ratio with filling speed for die filling with various electrostatic charges.
where n is a parameter related to the system configuration and filling environment, with a value generally between 1.0 and 1.6 (Schneider et al., 2007; Wu, 2008; Wu et al., 2003), and a value of n = 1.2 was found to be a good approximation for die filling with some powders (Wu et al., 2003). The critical filling speed vc and the constatnt n can be determined by fitting the measured fill ratios at various filling speeds at which a fill ratio is less than unity and treating vc and n as the free fitting paramters, as shown by the solid lines in Fig. 6. The corresponding values of vc and n are shown in Figs. 7 and 8, respectively. It is clear that the critical filling speed decreases as the particle charge increases, indicating that once particles are charged oppositely, due to the attractive electrostatic forces, agglomerates are formed and the powder becomes more cohesive with a poor flowability. Consequently, a lower critical filling speed is induced. It also implies that the higher the electrostatic charge, the poorer the flowability of the powder. In addition, the critical filling speed also depends on the filling conditions. A higher critical filling speed is obtained for die filling in a vacuum than in air, when the electrostatic charge is relatively low (say <6 × 10−13 C for the cases
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that both the presence of air and electrostatic charge can affect the powder flow behaviour during die filling, which was quantitatively characterised using the fill ratio and critical filling speed, both generally decreasing as the electrostatic charge increases. When the electrostatic charge is low, electrostatic interaction is weak and strong air/particle interaction results in lower fill ratio and lower critical filling speed as compared to those in a vacuum. However, when the electrostatic charge is high, electrostatic interaction becomes dominant and the influence of air becomes insignificant so that similar fill ratios and critical filling speeds are obtained for die filling in air and in a vacuum.
References
Fig. 7. Critical filling speed c as a function of particle charge for die filling in a vacuum and in air.
Fig. 8. Parameter n as a function of particle charge for die filling in a vacuum and in air.
considered here), because the interaction between air and particles can reduce the flow of powder into the die (Wu & Cocks, 2006; Wu et al., 2003). However, when the electrostatic charge is sufficiently high (say >6 × 10−13 C), electrostatic interaction becomes dominant and the effect of air becomes insignificant. Consequently, the critical filling speeds in air and in a vacuum are similar. A similar pattern is also obtained for the parameter n. It is interesting that the value of n for die filling with low and moderate electrostatic charges in air obtained using DEM/CFD has a value around 1.2, which is consistent with the values obtained experimentally (Schneider et al., 2007; Wu et al., 2003). 4. Conclusions The effect of electrostatic charge on powder flow during die filling was examined using a modified DEM/CFD code implemented with long-range electrostatic interaction. Simulations of die filling with oppositely charged particles in air and in a vacuum reveal
Bailey, A. G. (1984). Electrostatic phenomena during powder handling. Powder Technology, 37, 71–85. Bailey, A. G. (1993). Charging of solids and powders. Journal of Electrostatics, 30, 167–180. Bierwisch, C., Kraft, T., Riedel, H., & Moseler, M. (2009). Die filling optimization using three-dimensional discrete element modeling. Powder Technology, 196(2), 169–179. Bocchini, G. F. (1987). Influence of small die width on filling and compacting densities. Powder Metallurgy, 30(4), 261–266. Elsdon, R., & Mitchell, F. R. G. (1976). Contact electrification of polymers. Journal of Physics D: Applied Physics, 9(10), 1445–1460. Engers, D. A., Fricke, M. N., Newman, A. W., & Morris, K. R. (2007). Triboelectric charging and dielectric properties of pharmaceutically relevant mixtures. Journal of Electrostatics, 65(9), 571–581. Glor, M. (1985). Hazards due to electrostatic charging of powders. Journal of Electrostatics, 16(2–3), 175–191. Grzybowski, B. A., Winkleman, A., Wiles, J. A., Brumer, Y., & Whitesides, G. M. (2003). Electrostatic self-assembly of macroscopic crystals using contact electrification. Nature Materials, 2(4), 241–245. Guo, Y., Kafui, K. D., Wu, C.-Y., Thornton, C., & Seville, J. P. K. (2009). A coupled DEM/CFD analysis of the effect of air on powder flow during die filling. AIChE Journal, 55(1), 49–62. Guo, Y., Wu, C.-Y., Kafui, K. D., & Thornton, C. (2010). Numerical analysis of densityinduced segregation during die filling. Powder Technology, 197(1–2), 111–119. Guo, Y., Wu, C.-Y., Kafui, K. D., & Thornton, C. (2011). 3D DEM/CFD analysis of sizeinduced segregation during die filling. Powder Technology, 206(1–2), 177–188. Guo, Y., Wu, C.-Y., & Thornton, C. (2011). The effects of air and particle density difference on segregation of powder mixtures during die filling. Chemical Engineering Science, 66(4), 661–673. Hjortsberg, E., & Bergquist, B. (2002). Filling induced density variations in metal powder. Powder Metallurgy, 45(2), 146–153. Hogue, M. D., Calle, C. I., Weitzman, P. S., & Curry, D. R. (2008). Calculating the trajectories of triboelectrically charged particles using Discrete Element Modeling (DEM). Journal of Electrostatics, 66(1–2), 32–38. Jaworek, A., Krupa, A., & Czech, T. (2007). Modern electrostatic devices and methods for exhaust gas cleaning: A brief review. Journal of Electrostatics, 65(3), 133–155. Kafui, K. D., Thornton, C., & Adams, M. J. (2002). Discrete particle-continuum fluid modelling of gas-solid fluidized beds. Chemical Engineering Science, 57(13), 2395–2410. Matsusaka, S., & Masuda, H. (2006). Simultaneous measurement of mass flow rate and charge-to-mass ratio of particles in gas-solids pipe flow. Chemical Engineering Science, 61, 2254–2261. Matsusaka, S., Maruyama, H., Matsuyama, T., & Ghadiri, M. (2010). Triboelectric charging of powders: A review. Chemical Engineering Science, 65, 5781–5807. Pei, C., Wu, C.-Y., Byard, S., & England, D. (2010). Numerical analysis of electrostatic effects during powder deposition using DEM/CFD. Journal of Pharmacy and Pharmacology, 62(10), 1454–1455. Pingali, K. C., Shinbrot, T., Hammond, S. V., & Muzzio, F. J. (2009). An observed correlation between flow and electrical properties of pharmaceutical blends. Powder Technology, 192(2), 157–165. Rice, E. R., & Tengzelius, J. (1986). Die filling characteristics of metal powders. Powder Metallurgy, 29(3), 183–194. Rowley, G. (2001). Quantifying electrostatic interactions in pharmaceutical solid systems. International Journal of Pharmaceutics, 227(1–2), 47–55. Schneider, L. C. R., Sinka, I. C., & Cocks, A. C. F. (2007). Characterisation of the flow behaviour of pharmaceutical powders using a model die-shoe filling system. Powder Technology, 173(1), 59–71. Seville, J. P. K., Tuzun, U., & Clift, R. (1997). Processing of particulate solids. London: Blackie Academic & Professional. Sinka, I. C., Schneider, L. C. R., & Cocks, A. C. F. (2004). Measurement of the flow properties of powders with special reference to die fill. International Journal of Pharmaceutics, 280(1–2), 27–38. Takeuchi, M. (2008). Improvement of charging characteristics of coating powders in electrostatic powder coating system. Journal of Physics: Conference Series, 142, 012065.
E.N. Nwose et al. / Particuology 10 (2012) 229–235 Tsuji, Y., Kawaguchi, T., & Tanaka, T. (1993). Discrete particle simulation of twodimensional fluidized bed. Powder Technology, 77(1), 79–87. Watanabe, H., Ghadiri, M., Matsuyama, T., Ding, Y. L., Pitt, K. G., Maruyama, H., et al. (2007). Triboelectrification of pharmaceutical powders by particle impact. International Journal of Pharmaceutics, 334(1–2), 149–155. Watano, S. (2006). Mechanism and control of electrification in pneumatic conveying of powders. Chemical Engineering Science, 61, 2271–2278. Wu, C.-Y. (2008). DEM simulations of die filling during pharmaceutical tabletting. Particuology, 6(6), 412–418. Wu, C.-Y., Dihoru, L., & Cocks, A. C. F. (2003). The flow of powder into simple and stepped dies. Powder Technology, 134(1–2), 24–39.
235
Wu, C.-Y., & Guo, Y. (2010). Modelling of the flow of cohesive powders during pharmaceutical tabletting. Journal of Pharmacy and Pharmacology, 62(10), 1450–1451. Wu, C.-Y., & Cocks, A. C. F. (2006). Numerical and experimental investigations of the flow of powder into a confined space. Mechanics of Materials, 38(4), 304–324. Yu, A. B., & Xu, B. H. (2003). Particle-scale modelling of gas-solid flow in fluidisation. Journal of Chemical Technology and Biotechnology, 78(2–3), 111–121. Yu, S., Guo, Y., & Wu, C.-Y. (2009). DEM/CFD modelling of the deposition of dilute granular systems in a vertical container. Chinese Science Bulletin, 54(23), 4318–4326.
Contents lists available at SciVerse ScienceDirect
Particuology journal homepage: www.elsevier.com/locate/partic
Modelling die filling with charged particles using DEM/CFD Emmanuel Nkem Nwose, Chunlei Pei, Chuan-Yu Wu ∗ School of Chemical Engineering, University of Birmingham, Birmingham B15 2TT, UK
a r t i c l e
i n f o
Article history: Received 4 October 2011 Received in revised form 22 November 2011 Accepted 26 November 2011 Keywords: DEM CFD Electrostatics Die filling Powder flow Cohesion Charged particles
a b s t r a c t The effects of electrostatic charge on powder flow behaviour during die filling in a vacuum and in air were analysed using a coupled discrete element method and computational fluid dynamics (DEM/CFD) code, in which long range electrostatic interactions were implemented. The present 2D simulations revealed that both electrostatic charge and the presence of air can affect the powder flow behaviour during die filling. It was found that the electrostatic charge inhibited the flow of powders into the die and induced a loose packing structure. At the same filling speed, increasing the electrostatic charge led to a decrease in the fill ratio which quantifies the volumetric occupancy of powder in the die. In addition, increasing the shoe speed caused a further decrease in the fill ratio, which was characterised using the concept of critical filling speed. When the electrostatic charge was low, the air/particle interaction was strong so that a lower critical filling speed was obtained for die filling in air than in a vacuum. With high electrostatic charge, the electrostatic interactions became dominant. Consequently, similar fill ratio and critical filling speed were obtained for die filling in air and in a vacuum. © 2012 Chinese Society of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
1. Introduction Powders are common materials handled in various industries, such as food, chemical, metallurgical, pharmaceutical, agricultural and ceramic industries (Wu, 2008). It is well recognised that a number of factors, such as powder properties, processing conditions and the equipment design, affect powder flow behaviour (Schneider, Sinka, & Cocks, 2007). For instance, mixing powders in a humid environment will potentially cause stickiness and could lead to agglomeration and consequently degradation of products. In addition, during powder handling and processing, the use of multiple blends of crystalline powders and the inclusion of additives make powder blends prone to be electrostatically charged through contact electrification and polarisation (Bailey, 1984, 1993; Elsdon & Mitchell, 1976; Engers, Fricke, Newman, & Morris, 2007; Pingali, Shinbrot, Hammond, & Muzzio, 2009). In a number of powder handling processes, such as hopper discharge, grinding, sieving, mixing, fluidisation and conveying, the electrostatic charge can be transferred from a particle to its neighbouring particles or walls through the exchange of electrons, ions or materials (Matsusaka, Maruyama, Matsuyama, & Ghadiri, 2010). Once the particles in a powder get charged, attraction or repulsion can occur due to electrostatic interactions. The electrostatic
∗ Corresponding author. Tel.: +44 121 4145365; fax: +44 121 4145324. E-mail address: [email protected] (C.-Y. Wu).
interaction, on one hand, can be utilised to facilitate processing of powders, for example, in gas cleaning using electrostatic precipitators (Jaworek, Krupa, & Czech, 2007) and electrostatic coating (Takeuchi, 2008). On the other hand, it can lead to detrimental consequences, such as increasing the flow instability of powders as frequently observed in practice (Bailey, 1984; Engers et al., 2007; Glor, 1985; Pingali et al., 2009), and dust explosion due to the accumulation of excessive electrostatic charges (Bailey, 1993; Glor, 1985). It is hence necessary to consider the effect of electrostatics in powder handling and processing practice, as demonstrated by Matsusaka and Masuda (2006), who showed that the inclusion of electrostatic charges gave a better approximation of the apropos powder flow rate through a pipe. It is well recognized that the powder flow behaviour during die filling controls the quality of products manufactured through powder compaction (Bocchini, 1987; Hjortsberg & Bergquist, 2002; Rice & Tengzelius, 1986; Schneider et al., 2007; Wu, 2008; Wu, Dihoru, & Cocks, 2003), which is a typical manufacture process in pharmaceutical, ceramic and powder metallurgy industries, and typically involves three distinctive stages: die filling, compaction and ejection (Wu, 2008). Although die filling has been intensively investigated experimentally and numerically (Bierwisch, Kraft, Riedel, & Moseler, 2009; Guo, Kafui, Wu, Thornton, & Seville, 2009; Guo, Wu, Kafui, & Thornton, 2010; Guo, Wu, Kafui, & Thornton, 2011; Guo, Wu, & Thornton, 2011; Schneider et al., 2007; Wu, 2008; Wu et al., 2003; Wu & Guo, 2010), little attention has been paid to how electrostatics affects the powder flow behaviour during die
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doi:10.1016/j.partic.2011.11.010
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filling. Therefore, in this study, the flow of charged powders during die filling was explored using a modified DEM/CFD, in which long range electrostatic interactions were considered. How the electrostatic charge affects the powder behaviour during die filling was examined in detail.
2. DEM/CFD DEM/CFD is a coupled numerical method that adapts an Eulerian–Lagrangian approach in modelling solid/gas and solid/fluid two phase particulate flows (Kafui, Thornton, & Adams, 2002; Tsuji, Kawaguchi, & Tanaka, 1993; Yu & Xu, 2003). In DEM/CFD, the motion of particles is modelled using DEM while the flow of gases or fluids is solved using CFD. The interactions between particles and gases/fluids are considered and two-way coupling is implemented so that how the motion of particles affects the gas or fluid flow is considered, so is the effect of fluid flow on the motion of particles. The DEM/CFD has been approved as a robust method for modelling two phase flows involving particles (Guo et al., 2009, 2010; Guo, Wu, Kafui, et al., 2011; Guo, Wu, et al., 2011; Kafui et al., 2002; Tsuji et al., 1993; Wu & Guo, 2010; Yu, Guo, & Wu, 2009; Yu & Xu, 2003). It has also been successfully used to model die filling in the presence of air (Guo et al., 2009, 2010; Guo, Wu, Kafui, et al., 2011; Guo, Wu, et al., 2011; Wu & Guo, 2010). In addition, DEM was also modified to model flow of charged particles (Hogue, Calle, Weitzman, & Curry, 2008; Pei, Wu, Byard, & England, 2010; Watano, 2006). Watano (2006) developed a DEM with a simplified electrification model that assumes the charge of a particle to be proportional to the normal contact velocity and the number of collisions, and explored the flow of electrostatically charged powder in a pneumatic conveyor system. Hogue et al. (2008) analysed the flow of particles rolling down an inclined plane using a DEM with a time-dependent electrification model. Pei et al. (2010) incorporated electrostatic interactions into the DEM/CFD developed by Kafui et al. (2002) and modelled the deposition of charged particles in a tube in the presence of air.
2.1. DEM/CFD with electrostatics In this study, the model developed by Pei et al. (2010) was employed to model the die filling with charged particles. The interactions between elastic particles are modelled using Hertz theory in the normal direction and the theory of Mindlin and Deresiewicz in the tangential direction (Kafui et al., 2002). In this modified DEM/CFD model, a truncation method with a pre-defined cut-off distance is implemented for detecting the long-range electrostatic interactions between objects. When the distance between two objects is larger than the cut-off distance, the electrostatic interaction is ignored, which is similar to those employed by others (Hogue et al., 2008; Watano, 2006). Within the cut-off distance, the electrostatic force between particles is modelled using the Coulomb’s law (Seville, Tuzun, & Clift, 1997) as follow: F21 =
1 q1 q2 rˆ 21 , 4ε0 εr r 2 21
(1)
where F21 is the electrostatic force from particle 2 to particle 1, ε0 is the permittivity of free space, εr is the relative permittivity of the medium in the vicinity of the particles, q1 and q2 are the values of charges on the two particles, r21 is the distance between the r21 is the unit vector from particle centres of the two particles and ˆ 2 to particle 1.
Fig. 1. Model set up for die filling.
The interaction between a charged particle and a surface within the cut-off distance is modelled using an imaging force (Seville et al., 1997): Fimg =
1 Q2 aˆ , 4ε0 εr (2a)2
(2)
where Fimg is the image force of the particle towards the neutral inductive surface, Q is the value of the charges on the particle, a is the distance between the centre of the particle and the neutral ˆ is the unit vector from the particle to the inductive surface and a neutral inductive surface. Using the truncation method, it is critical to set an appropriate cut-off distance as the longer the cut-off distance, the more accurate the electrostatic interaction is modelled, but the more expensive the computation is. Although a short cut-off distance leads to faster computing, it may induce significant numerical errors as a large amount of electrostatic interactions is ignored. In this study, the cut off distance is set to 10 times the particle radius, which is sufficiently large for the cases considered. The Newton’s equation of motion was used to calculate the velocity, position and acceleration of the particles once all interaction forces, including the long-range electrostatic forces, mechanical contact forces, air-drag forces and so on, are determined. 2.2. DEM/CFD model for die filling The modified DEM/CFD model with electrostatic interaction was used to simulate die filling in air and in a vacuum in 2D, which is less computation intensive and easier for data visualising and process understanding, compared to 3D simulations. The DEM/CFD model for die filling is shown in Fig. 1. The model consisted of a shoe (9.0 mm wide and 14.0 mm high), and a die (2.0 mm wide and 3.0 mm high). In this study, only passive die filling (i.e. a moving shoe was utilised while the die remained stationary) was analysed. The shoe sat above a platform and moved from right to left at a specified filling speed ranging from 0.08 to 0.40 m/s in this study, which was similar to the typical die filling speed used in practice (Wu, 2008). The powder was modelled as an assembly of mono-sized particles of 100 m in diameter. Die filling simulations with 1000 mono-sized particles were reported here. Preliminary studies with 5000 particles for some typical cases were also performed and similar results were obtained. It was believed that 1000 particles were sufficient for the cases considered here. For die filling
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Table 1 Simulation parameters. Parameter Particle properties Particle diameter (m) Particle density (kg/m3 ) Young’s modulus (Pa) Poisson’s ratio Vessel properties Density (kg/m3 ) Young’s modulus (Pa) Poisson’s ratio Interaction properties Inter-particle friction coefficient Particle/wall friction coefficient Gas properties Shear viscosity (Pa s) Temperature (K) Average molar mass (kg/mol) Pressure (Pa)
Value 100 1500 8.70 × 109 0.30 7900 210 × 109 0.30 0.30 0.30 1.8 × 10−5 293 2.88 × 10−2 1.01325 × 105
with charged particles, 500 particles were assumed to be charged positively, while the other 500 were negatively charged. In each simulation, all particles had the same magnitude of charge. In order to explore the influence of electrostatic charge on die filling behaviour, the particle charge was systematically varied between 0.0 and 1.0 × 10−12 C, which are the typical values of charges that pharmaceutical powders acquire during the handling processes (Rowley, 2001; Watanabe et al., 2007). For the particles, material properties of microcrystalline cellulose (MCC) were used, while the shoe, the die and the platform were assumed to be stainless steel. The simulation parameters are listed in Table 1. The explicit time step is 0.227 × 10−7 s. For the highest electrostatic charge (10 × 10−13 C) used in this study, the electrostatic force at its cutoff distance is more than 20 times smaller than the gravity of the particle. The particles were initially generated randomly inside the shoe and then settled onto the bottom of the shoe under gravity and electrostatic forces (for charged particles only). Once the particles settled in the shoe with a negligible kinetic energy, the shoe started to move at the specified filling speed. When it traversed over the die, some particles were deposited into the die. The simulation was terminated once the shoe passed the die and the deposited particles settled. 3. Results and discussion From DEM/CFD simulations, the positions and kinematics of individual particles were determined at different time instants, from which the overall flow patterns were obtained. The typical powder flow patterns are presented in Figs. 2–5. In addition, the average mass flow rate was determined by tracking the particles deposited into the die. Knowing the positions and the total number of deposited particles enabled the fill ratio, a parameter that was introduced to characterise the die filling behaviour (Sinka, Schneider, & Cocks, 2004; Wu, 2008; Wu & Cocks, 2006; Wu et al., 2003), to be determined. In this section, the effect of electrostatic charge on powder flow patterns during die filling was discussed, followed by an examination of the effect on the fill ratio. 3.1. Powder flow patterns The powder flow pattern during die filling with uncharged particles (q = 0 C) in air at a filling speed of 0.1 m/s is shown in Fig. 2. It is evident that at this particular speed a ‘nose’ shaped profile was formed when the powder in the shoe is delivered just over the die opening (Fig. 2(a)). This was defined as the nose flow by Wu et al. (2003), with which particles located at both the top free
Fig. 2. Powder flow patterns during die filling with un-charged particles (q = 0 C) in air at a filling speed of 0.1 m/s.
surface and the bottom of the powder bed were deposited into the die. As the shoe moved further, the flowing powder stream hit the far side of the die (the left wall) and flowed backwards (Fig. 2(b) and (c)). After the shoe passed the die opening, the die was almost completely filled (Fig. 2(d)). Although a similar powder flow pattern was observed for the die filling in a vacuum with the same powder at the same filling speed (Fig. 3), comparing Fig. 3 with Fig. 2 does reveal that the powder flow in a vacuum was faster than in air and more particles are deposited into the die in a vacuum (see Figs. 2(d) and 3(d)), indicating that the presence of air inhibits the powder flow during die filling. All these observations are in broad agreement with the experimental observations reported in the literature (Schneider et al., 2007; Wu & Cocks, 2006; Wu et al., 2003). As the filling speed was increased from 0.1 m/s (Fig. 2) to 0.2 m/s (Fig. 4), the powder bed in the shoe strode over the die opening quickly and covered the die (Fig. 4(a)). Consequently, only particles located at the bottom of the powder bed were deposited along the far side (i.e. the left wall) into the die (Fig. 4(b) and (c)). This is the so-called “bulk flow” (Wu et al., 2003), with which the flow is slow and the die filling processes dominated with bulk flow generally led to a partially die fill (i.e. the die was not completely filled with particles). This is further demonstrated from the present DEM/CFD simulations, as it was clear that the die was only partially filled (Fig. 4(d)) when the filling speed was increased to 0.2 m/s. Once the particles were charged oppositely, the electrostatic interaction promoted the formation of clusters of particles carrying
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Fig. 3. Powder flow patterns during die filling with un-charged particles (q = 0 C) in a vacuum at a filling speed of 0.1 m/s.
Fig. 4. Powder flow patterns during die filling with un-charged particles (q = 0 C) in air at a filling speed of 0.2 m/s.
opposite charges, as shown numerically (Pei et al., 2010) and experimentally (Grzybowski, Winkleman, Wiles, Brumer, & Whitesides, 2003). This is also observed in the present die filling simulations with oppositely charged particles as illustrated in Fig. 5. It can be seen that localised particle clusters were formed in the powder bed. In addition, the strong image forces between charged particles and the surfaces of the shoe and the die caused some particle sticking on the surfaces, as commonly observed in the powder handling practice. In addition, the strong electrostatic forces significantly prevented the particles from flowing into the die, as the particles were only scraped and squeezed along the far side into the die (Fig. 5(b) and (c)). Furthermore, the deposited particles stuck on the die wall and formed very loose packing structure as shown in Fig. 5(d).
bed in the die is constant, i.e. independent of the filling speed and die fill level, Eq. (3) can be rewritten as
3.2. The effect of electrostatic charge on the fill ratio Wu et al. (2003) introduced the fill ratio to characterise the packing behaviour of powders during die filling. The fill ratio was defined as the ratio of the volume of the powder bed to the die volume (Schneider et al., 2007; Sinka et al., 2004; Wu, 2008; Wu et al., 2003), i.e. ı=
˚p , ˚d
(3)
where ˚p and ˚d are respectively the volume of the powder bed and of the die. A fill ratio of a value of unity indicates that the die is completely filled. Assuming that the bulk density b of the powder
ı=
Mp , Md
(4)
where Mp and Md are the total powder mass deposited in the die at a specified filling speed and the powder mass of fully filled die, respectively. Eq. (4) provides a simple approach to determine the fill ratio, which has been used to analyse both experimental and numerical data (Schneider et al., 2007; Sinka et al., 2004; Wu, 2008; Wu et al., 2003). The fill ratios for die filling with powders of different electrostatic charges at various filling speeds in a vacuum and in air are presented in Fig. 6. It can be seen that the fill ratio generally decreases as the filling speed (i.e. the shoe speed) increases. At the same filling speed, it is also observed that the fill ratio decreases as the electrostatic charge increases, indicating that a poorer flow performance and a more cohesive system were induced once the powder acquires more electrostatic charges. Comparing the data shown in Fig. 6(a) (in a vacuum) and (b) (in air) reveals that a lower fill ratio is generally obtained for die filling in air than in a vacuum. However, the difference between the fill ratios in a vacuum and in air decreases as the electrostatic charge is increased. This is due to the fact that the presence of air generally inhibits the flow of powder into the die so that a low fill ratio is obtained compared to the filling in a vacuum (Wu & Cocks, 2006; Wu et al., 2003). However, once the particles are charged oppositely, they form large clusters/agglomerates due to the attractive electrostatic force,
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Fig. 5. Powder flow patterns during die filling with oppositely charged particles (q = 1.0 × 10−12 C) in air at a filling speed of 0.1 m/s.
especially with high electrostatic charges. Consequently, the effect of air becomes insignificant as a result of the increased agglomerate sizes when the charge is sufficiently high. The variation of fill ratio with filling speed can be further characterised using the concept of critical filling speed, which was defined as the highest filling speed at which the die can be completely filled (Wu, 2008; Wu et al., 2003). In other words, the die cannot be completely filled (i.e. ı < 1) if the filling speed is higher than the critical filling speed, while it can be completely filled (i.e. ı = 1) if the speed is lower than the critical filling speed. We hence have ı = 1 for vs ≤ vc for vs > vc
ı < 1,
(5a) (5b)
where vs and vc are the filling (shoe) speed and critical filling speed, respectively. The critical filling speed is proved to be a useful parameter for characterising the flowability of powders during die filling (Schneider et al., 2007; Sinka et al., 2004; Wu et al., 2003). A higher critical filling speed indicates better flowability so that faster filling can be accomplished, while a lower critical filling speed implies poorer powder flowability and slower filling has to be employed to ensure complete fill of the die. For die filling at high speeds (vs ≥ vc ), Wu et al. (2003) developed a model assuming that powder flow into a die was a steady flow and proposed that the fill ratio can be related to the filling speed and the critical filling speed by ı=
v n c
vs
,
for vs = vc
(6)
Fig. 6. Variation of filling ratio with filling speed for die filling with various electrostatic charges.
where n is a parameter related to the system configuration and filling environment, with a value generally between 1.0 and 1.6 (Schneider et al., 2007; Wu, 2008; Wu et al., 2003), and a value of n = 1.2 was found to be a good approximation for die filling with some powders (Wu et al., 2003). The critical filling speed vc and the constatnt n can be determined by fitting the measured fill ratios at various filling speeds at which a fill ratio is less than unity and treating vc and n as the free fitting paramters, as shown by the solid lines in Fig. 6. The corresponding values of vc and n are shown in Figs. 7 and 8, respectively. It is clear that the critical filling speed decreases as the particle charge increases, indicating that once particles are charged oppositely, due to the attractive electrostatic forces, agglomerates are formed and the powder becomes more cohesive with a poor flowability. Consequently, a lower critical filling speed is induced. It also implies that the higher the electrostatic charge, the poorer the flowability of the powder. In addition, the critical filling speed also depends on the filling conditions. A higher critical filling speed is obtained for die filling in a vacuum than in air, when the electrostatic charge is relatively low (say <6 × 10−13 C for the cases
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that both the presence of air and electrostatic charge can affect the powder flow behaviour during die filling, which was quantitatively characterised using the fill ratio and critical filling speed, both generally decreasing as the electrostatic charge increases. When the electrostatic charge is low, electrostatic interaction is weak and strong air/particle interaction results in lower fill ratio and lower critical filling speed as compared to those in a vacuum. However, when the electrostatic charge is high, electrostatic interaction becomes dominant and the influence of air becomes insignificant so that similar fill ratios and critical filling speeds are obtained for die filling in air and in a vacuum.
References
Fig. 7. Critical filling speed c as a function of particle charge for die filling in a vacuum and in air.
Fig. 8. Parameter n as a function of particle charge for die filling in a vacuum and in air.
considered here), because the interaction between air and particles can reduce the flow of powder into the die (Wu & Cocks, 2006; Wu et al., 2003). However, when the electrostatic charge is sufficiently high (say >6 × 10−13 C), electrostatic interaction becomes dominant and the effect of air becomes insignificant. Consequently, the critical filling speeds in air and in a vacuum are similar. A similar pattern is also obtained for the parameter n. It is interesting that the value of n for die filling with low and moderate electrostatic charges in air obtained using DEM/CFD has a value around 1.2, which is consistent with the values obtained experimentally (Schneider et al., 2007; Wu et al., 2003). 4. Conclusions The effect of electrostatic charge on powder flow during die filling was examined using a modified DEM/CFD code implemented with long-range electrostatic interaction. Simulations of die filling with oppositely charged particles in air and in a vacuum reveal
Bailey, A. G. (1984). Electrostatic phenomena during powder handling. Powder Technology, 37, 71–85. Bailey, A. G. (1993). Charging of solids and powders. Journal of Electrostatics, 30, 167–180. Bierwisch, C., Kraft, T., Riedel, H., & Moseler, M. (2009). Die filling optimization using three-dimensional discrete element modeling. Powder Technology, 196(2), 169–179. Bocchini, G. F. (1987). Influence of small die width on filling and compacting densities. Powder Metallurgy, 30(4), 261–266. Elsdon, R., & Mitchell, F. R. G. (1976). Contact electrification of polymers. Journal of Physics D: Applied Physics, 9(10), 1445–1460. Engers, D. A., Fricke, M. N., Newman, A. W., & Morris, K. R. (2007). Triboelectric charging and dielectric properties of pharmaceutically relevant mixtures. Journal of Electrostatics, 65(9), 571–581. Glor, M. (1985). Hazards due to electrostatic charging of powders. Journal of Electrostatics, 16(2–3), 175–191. Grzybowski, B. A., Winkleman, A., Wiles, J. A., Brumer, Y., & Whitesides, G. M. (2003). Electrostatic self-assembly of macroscopic crystals using contact electrification. Nature Materials, 2(4), 241–245. Guo, Y., Kafui, K. D., Wu, C.-Y., Thornton, C., & Seville, J. P. K. (2009). A coupled DEM/CFD analysis of the effect of air on powder flow during die filling. AIChE Journal, 55(1), 49–62. Guo, Y., Wu, C.-Y., Kafui, K. D., & Thornton, C. (2010). Numerical analysis of densityinduced segregation during die filling. Powder Technology, 197(1–2), 111–119. Guo, Y., Wu, C.-Y., Kafui, K. D., & Thornton, C. (2011). 3D DEM/CFD analysis of sizeinduced segregation during die filling. Powder Technology, 206(1–2), 177–188. Guo, Y., Wu, C.-Y., & Thornton, C. (2011). The effects of air and particle density difference on segregation of powder mixtures during die filling. Chemical Engineering Science, 66(4), 661–673. Hjortsberg, E., & Bergquist, B. (2002). Filling induced density variations in metal powder. Powder Metallurgy, 45(2), 146–153. Hogue, M. D., Calle, C. I., Weitzman, P. S., & Curry, D. R. (2008). Calculating the trajectories of triboelectrically charged particles using Discrete Element Modeling (DEM). Journal of Electrostatics, 66(1–2), 32–38. Jaworek, A., Krupa, A., & Czech, T. (2007). Modern electrostatic devices and methods for exhaust gas cleaning: A brief review. Journal of Electrostatics, 65(3), 133–155. Kafui, K. D., Thornton, C., & Adams, M. J. (2002). Discrete particle-continuum fluid modelling of gas-solid fluidized beds. Chemical Engineering Science, 57(13), 2395–2410. Matsusaka, S., & Masuda, H. (2006). Simultaneous measurement of mass flow rate and charge-to-mass ratio of particles in gas-solids pipe flow. Chemical Engineering Science, 61, 2254–2261. Matsusaka, S., Maruyama, H., Matsuyama, T., & Ghadiri, M. (2010). Triboelectric charging of powders: A review. Chemical Engineering Science, 65, 5781–5807. Pei, C., Wu, C.-Y., Byard, S., & England, D. (2010). Numerical analysis of electrostatic effects during powder deposition using DEM/CFD. Journal of Pharmacy and Pharmacology, 62(10), 1454–1455. Pingali, K. C., Shinbrot, T., Hammond, S. V., & Muzzio, F. J. (2009). An observed correlation between flow and electrical properties of pharmaceutical blends. Powder Technology, 192(2), 157–165. Rice, E. R., & Tengzelius, J. (1986). Die filling characteristics of metal powders. Powder Metallurgy, 29(3), 183–194. Rowley, G. (2001). Quantifying electrostatic interactions in pharmaceutical solid systems. International Journal of Pharmaceutics, 227(1–2), 47–55. Schneider, L. C. R., Sinka, I. C., & Cocks, A. C. F. (2007). Characterisation of the flow behaviour of pharmaceutical powders using a model die-shoe filling system. Powder Technology, 173(1), 59–71. Seville, J. P. K., Tuzun, U., & Clift, R. (1997). Processing of particulate solids. London: Blackie Academic & Professional. Sinka, I. C., Schneider, L. C. R., & Cocks, A. C. F. (2004). Measurement of the flow properties of powders with special reference to die fill. International Journal of Pharmaceutics, 280(1–2), 27–38. Takeuchi, M. (2008). Improvement of charging characteristics of coating powders in electrostatic powder coating system. Journal of Physics: Conference Series, 142, 012065.
E.N. Nwose et al. / Particuology 10 (2012) 229–235 Tsuji, Y., Kawaguchi, T., & Tanaka, T. (1993). Discrete particle simulation of twodimensional fluidized bed. Powder Technology, 77(1), 79–87. Watanabe, H., Ghadiri, M., Matsuyama, T., Ding, Y. L., Pitt, K. G., Maruyama, H., et al. (2007). Triboelectrification of pharmaceutical powders by particle impact. International Journal of Pharmaceutics, 334(1–2), 149–155. Watano, S. (2006). Mechanism and control of electrification in pneumatic conveying of powders. Chemical Engineering Science, 61, 2271–2278. Wu, C.-Y. (2008). DEM simulations of die filling during pharmaceutical tabletting. Particuology, 6(6), 412–418. Wu, C.-Y., Dihoru, L., & Cocks, A. C. F. (2003). The flow of powder into simple and stepped dies. Powder Technology, 134(1–2), 24–39.
235
Wu, C.-Y., & Guo, Y. (2010). Modelling of the flow of cohesive powders during pharmaceutical tabletting. Journal of Pharmacy and Pharmacology, 62(10), 1450–1451. Wu, C.-Y., & Cocks, A. C. F. (2006). Numerical and experimental investigations of the flow of powder into a confined space. Mechanics of Materials, 38(4), 304–324. Yu, A. B., & Xu, B. H. (2003). Particle-scale modelling of gas-solid flow in fluidisation. Journal of Chemical Technology and Biotechnology, 78(2–3), 111–121. Yu, S., Guo, Y., & Wu, C.-Y. (2009). DEM/CFD modelling of the deposition of dilute granular systems in a vertical container. Chinese Science Bulletin, 54(23), 4318–4326.